Ramakrishnan

Ramakrishnan Vaidyanathan

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7 years, 74 days

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With twenty years of Industrial experience and twenty years of teaching experience, I am now as retired Professor, using Maple to teach mathematics subject for students studying X to XII standards. Published XII Mathematics books.

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These are answers submitted by Ramakrishnan

Hope attached doc gives an expanded answer with 12 RF terms would be an acceptable solution.

Thanks. Ramakrishnan V

Fractional_terms_of_an_epression.mw
 

sqrt(Dp)*(-Dp*sqrt(s+thetac)*alpha1*pinf*s^2-2*Dp*sqrt(s+thetac)*alpha1*pinf*s*thetac-Dp*sqrt(s+thetac)*alpha1*pinf*thetac^2+A2*Dp*sqrt(s+thetac)*alpha1*s+A2*Dp*sqrt(s+thetac)*alpha1*thetac+Dc*sqrt(s+thetac)*alpha1*pinf*s^2+Dc*sqrt(s+thetac)*alpha1*pinf*s*thetac+A1*Dc*alpha1*s^2+A1*Dc*alpha1*s*thetac+A1*sqrt(Dc)*sqrt(s+thetac)*s^2+A1*sqrt(Dc)*sqrt(s+thetac)*s*thetac-A2*Dc*sqrt(s+thetac)*alpha1*s)*exp((-lh+x)*sqrt(s)/sqrt(Dp))/((s+thetac)^(3/2)*s*(Dc*s-Dp*s-Dp*thetac)*(-sqrt(Dp)*alpha1+sqrt(s)))

Dp^(1/2)*(-Dp*(s+thetac)^(1/2)*alpha1*pinf*s^2-2*Dp*(s+thetac)^(1/2)*alpha1*pinf*s*thetac-Dp*(s+thetac)^(1/2)*alpha1*pinf*thetac^2+A2*Dp*(s+thetac)^(1/2)*alpha1*s+A2*Dp*(s+thetac)^(1/2)*alpha1*thetac+Dc*(s+thetac)^(1/2)*alpha1*pinf*s^2+Dc*(s+thetac)^(1/2)*alpha1*pinf*s*thetac+A1*Dc*alpha1*s^2+A1*Dc*alpha1*s*thetac+A1*Dc^(1/2)*(s+thetac)^(1/2)*s^2+A1*Dc^(1/2)*(s+thetac)^(1/2)*s*thetac-A2*Dc*(s+thetac)^(1/2)*alpha1*s)*exp((-lh+x)*s^(1/2)/Dp^(1/2))/((s+thetac)^(3/2)*s*(Dc*s-Dp*s-Dp*thetac)*(-Dp^(1/2)*alpha1+s^(1/2)))

(1)

``

simplify(Dp^(1/2)*(-Dp*(s+thetac)^(1/2)*alpha1*pinf*s^2-2*Dp*(s+thetac)^(1/2)*alpha1*pinf*s*thetac-Dp*(s+thetac)^(1/2)*alpha1*pinf*thetac^2+A2*Dp*(s+thetac)^(1/2)*alpha1*s+A2*Dp*(s+thetac)^(1/2)*alpha1*thetac+Dc*(s+thetac)^(1/2)*alpha1*pinf*s^2+Dc*(s+thetac)^(1/2)*alpha1*pinf*s*thetac+A1*Dc*alpha1*s^2+A1*Dc*alpha1*s*thetac+A1*Dc^(1/2)*(s+thetac)^(1/2)*s^2+A1*Dc^(1/2)*(s+thetac)^(1/2)*s*thetac-A2*Dc*(s+thetac)^(1/2)*alpha1*s)*exp((-lh+x)*s^(1/2)/Dp^(1/2))/((s+thetac)^(3/2)*s*(Dc*s-Dp*s-Dp*thetac)*(-Dp^(1/2)*alpha1+s^(1/2))))

exp((-lh+x)*s^(1/2)/Dp^(1/2))*((s*A1*(s+thetac)*Dc^(1/2)+((Dc-Dp)*s-Dp*thetac)*(pinf*s+pinf*thetac-A2)*alpha1)*(s+thetac)^(1/2)+s*A1*Dc*alpha1*(s+thetac))*Dp^(1/2)/((s+thetac)^(3/2)*(-Dp^(1/2)*alpha1+s^(1/2))*((Dc-Dp)*s-Dp*thetac)*s)

(2)

``

The above  expression  (2) is a simple fraction answer. To expand in separate terms we expand the numerator separately and divide by the denominator.

Expansion of numerator follows.

exp((-lh+x)*sqrt(s)/sqrt(Dp))*((s*A1*(s+thetac)*sqrt(Dc)+((Dc-Dp)*s-Dp*thetac)*(pinf*s+pinf*thetac-A2)*alpha1)*sqrt(s+thetac)+s*A1*Dc*alpha1*(s+thetac))*sqrt(Dp)
"(=)"
-exp((-lh+x)*s^(1/2)/Dp^(1/2))*Dp^(3/2)*(s+thetac)^(1/2)*alpha1*pinf*s^2-2*exp((-lh+x)*s^(1/2)/Dp^(1/2))*Dp^(3/2)*(s+thetac)^(1/2)*alpha1*pinf*s*thetac-exp((-lh+x)*s^(1/2)/Dp^(1/2))*Dp^(3/2)*(s+thetac)^(1/2)*alpha1*pinf*thetac^2+exp((-lh+x)*s^(1/2)/Dp^(1/2))*Dp^(3/2)*A2*(s+thetac)^(1/2)*alpha1*s+exp((-lh+x)*s^(1/2)/Dp^(1/2))*Dp^(3/2)*A2*(s+thetac)^(1/2)*alpha1*thetac+exp((-lh+x)*s^(1/2)/Dp^(1/2))*Dp^(1/2)*Dc*(s+thetac)^(1/2)*alpha1*pinf*s^2+exp((-lh+x)*s^(1/2)/Dp^(1/2))*Dp^(1/2)*Dc*(s+thetac)^(1/2)*alpha1*pinf*s*thetac+exp((-lh+x)*s^(1/2)/Dp^(1/2))*Dp^(1/2)*A1*Dc*alpha1*s^2+exp((-lh+x)*s^(1/2)/Dp^(1/2))*Dp^(1/2)*A1*Dc*alpha1*s*thetac+exp((-lh+x)*s^(1/2)/Dp^(1/2))*Dp^(1/2)*A1*Dc^(1/2)*(s+thetac)^(1/2)*s^2+exp((-lh+x)*s^(1/2)/Dp^(1/2))*Dp^(1/2)*A1*Dc^(1/2)*(s+thetac)^(1/2)*s*thetac-exp((-lh+x)*s^(1/2)/Dp^(1/2))*Dp^(1/2)*A2*Dc*(s+thetac)^(1/2)*alpha1*s

``

Division by denominator follows.

[-exp((-lh+x)*sqrt(s)/sqrt(Dp))*Dp^(3/2)*sqrt(s+thetac)*alpha1*pinf*s^2-2*exp((-lh+x)*sqrt(s)/sqrt(Dp))*Dp^(3/2)*sqrt(s+thetac)*alpha1*pinf*s*thetac-exp((-lh+x)*sqrt(s)/sqrt(Dp))*Dp^(3/2)*sqrt(s+thetac)*alpha1*pinf*thetac^2+exp((-lh+x)*sqrt(s)/sqrt(Dp))*Dp^(3/2)*A2*sqrt(s+thetac)*alpha1*s+exp((-lh+x)*sqrt(s)/sqrt(Dp))*Dp^(3/2)*A2*sqrt(s+thetac)*alpha1*thetac+exp((-lh+x)*sqrt(s)/sqrt(Dp))*sqrt(Dp)*Dc*sqrt(s+thetac)*alpha1*pinf*s^2+exp((-lh+x)*sqrt(s)/sqrt(Dp))*sqrt(Dp)*Dc*sqrt(s+thetac)*alpha1*pinf*s*thetac+exp((-lh+x)*sqrt(s)/sqrt(Dp))*sqrt(Dp)*A1*Dc*alpha1*s^2+exp((-lh+x)*sqrt(s)/sqrt(Dp))*sqrt(Dp)*A1*Dc*alpha1*s*thetac+exp((-lh+x)*sqrt(s)/sqrt(Dp))*sqrt(Dp)*A1*sqrt(Dc)*sqrt(s+thetac)*s^2+exp((-lh+x)*sqrt(s)/sqrt(Dp))*sqrt(Dp)*A1*sqrt(Dc)*sqrt(s+thetac)*s*thetac-exp((-lh+x)*sqrt(s)/sqrt(Dp))*sqrt(Dp)*A2*Dc*sqrt(s+thetac)*alpha1*s]/((s+thetac)^(3/2)*(-sqrt(Dp)*alpha1+sqrt(s))*((Dc-Dp)*s-Dp*thetac)*s)

[-exp((-lh+x)*s^(1/2)/Dp^(1/2))*Dp^(3/2)*(s+thetac)^(1/2)*alpha1*pinf*s^2-2*exp((-lh+x)*s^(1/2)/Dp^(1/2))*Dp^(3/2)*(s+thetac)^(1/2)*alpha1*pinf*s*thetac-exp((-lh+x)*s^(1/2)/Dp^(1/2))*Dp^(3/2)*(s+thetac)^(1/2)*alpha1*pinf*thetac^2+exp((-lh+x)*s^(1/2)/Dp^(1/2))*Dp^(3/2)*A2*(s+thetac)^(1/2)*alpha1*s+exp((-lh+x)*s^(1/2)/Dp^(1/2))*Dp^(3/2)*A2*(s+thetac)^(1/2)*alpha1*thetac+exp((-lh+x)*s^(1/2)/Dp^(1/2))*Dp^(1/2)*Dc*(s+thetac)^(1/2)*alpha1*pinf*s^2+exp((-lh+x)*s^(1/2)/Dp^(1/2))*Dp^(1/2)*Dc*(s+thetac)^(1/2)*alpha1*pinf*s*thetac+exp((-lh+x)*s^(1/2)/Dp^(1/2))*Dp^(1/2)*A1*Dc*alpha1*s^2+exp((-lh+x)*s^(1/2)/Dp^(1/2))*Dp^(1/2)*A1*Dc*alpha1*s*thetac+exp((-lh+x)*s^(1/2)/Dp^(1/2))*Dp^(1/2)*A1*Dc^(1/2)*(s+thetac)^(1/2)*s^2+exp((-lh+x)*s^(1/2)/Dp^(1/2))*Dp^(1/2)*A1*Dc^(1/2)*(s+thetac)^(1/2)*s*thetac-exp((-lh+x)*s^(1/2)/Dp^(1/2))*Dp^(1/2)*A2*Dc*(s+thetac)^(1/2)*alpha1*s]/((s+thetac)^(3/2)*(-Dp^(1/2)*alpha1+s^(1/2))*((Dc-Dp)*s-Dp*thetac)*s)

(3)

``

This gives an expanded version of the expression in fractions. 12 terms are there.

``


 

Download Fractional_terms_of_an_epression.mw

 

I attach an excel doc with solution pairs for various x values. y and z value for a given x can be obtained from table or graph.

Hope this is useful

Ramakrishnan Vxyz_values.xlsx

This will have umpteen solutions. Please see attached doc where unapply command used to obtain set of solutions. z vs y and x vs y.

Hope tis ok. Ramakrishnan V
 

equnA := 37320/(.44)-1.1*y = z

84818.18183-1.1*y = 0.3e-4

(1)

fnc3 := unapply(37320/(.44)-1.1*y, y)

proc (y) options operator, arrow; 84818.18183-1.1*y end proc

(2)

37320/(.44)

84818.18183

(3)

37320/(.44*1.1)

77107.43800

(4)

``

``

The plot gives z values for y varying from 77107 to 77108 for values of z from -0.5 to 1.5

p3 := plot(fnc3, 77107 .. 77108)

 

equnB := 37320-y = x

37320-y = -39787.438

(5)

fnc4 := unapply(37320-y, y)

proc (y) options operator, arrow; 37320-y end proc

(6)

p4 := plot(fnc4, 77107 .. 77108)

 

``

``

At y:=77107.438;

z := 37320/(.44)-1.1*77107.438

0.3e-4

(7)

 

x := 37320-77107.438

-39787.438

(8)

``


 

Download Two_equnsThreeUnknowns.mwTwo_equnsThreeUnknowns.mw

Dear Sir,

Hope my document attached herewith would help you programme the way you want with all inputs received as a list X.

Thanks for using.

Ramakrishnan VreadstatExample1.mw
 

``

X := action:-fun(3)

[1, 2], 3, 4, 5

(1)

a := X[1, 1]

1

(2)

b := X[1, 2]

2

(3)

x[1] := X[2]

3

(4)

x2 := X[3]

4

(5)

x3 := X[4]

5

(6)

``


 

Download readstatExample1.mw

 

Please find attached my doc where in there is no error on procedure call.I have made dt as local and included the proc inside module.
 

 

``

a := readstat("x will be assigned ") 

45

(1)

b := readstat("x will be assigned ") = 45NULL

for i to 3 do x[i] := readstat("insert x") end do
 = 6

a := readstat("x will be assigned ") = 8NULL

b := readstat("x will be assigned ") = 9NULL

for i to 3 do x[i] := readstat("insert x") end do
 = 12

fun(3)

5

(4)

``


 

Download readstatExample.mwreadstatExample.mw

Hope this is fine with maple.

Ramakrishnan V

Please find attached document . Hope it can give all coefficients of the termscoefficients.mw
 

q(x, s) = -(-(-thetac*s^(3/2)-s^(5/2)+(s^2+s*thetac)*alpha1*sqrt(Dp))*Dc*A1*exp((lh-x)*sqrt(s+thetac)/sqrt(Dc))+((alpha1*(s+thetac)*(-pinf*s-pinf*thetac+A2)*Dp^(3/2)+s*sqrt(Dp)*(A1*(s+thetac)*sqrt(Dc)-Dc*alpha1*(-pinf*s-pinf*thetac+A2)))*sqrt(s+thetac)+A1*sqrt(Dp)*s*Dc*alpha1*(s+thetac))*exp(sqrt(s)*(-lh+x)/sqrt(Dp))-(-_F1(s)*(-s*alpha1*(s+thetac)^2*Dp^(3/2)-s^(3/2)*Dp*thetac^2+thetac*(Dc-2*Dp)*s^(5/2)+(Dc-Dp)*s^(7/2)+sqrt(Dp)*s^2*Dc*alpha1*(s+thetac))*exp((-2*lh+x)*sqrt(s)/sqrt(Dp))+_F1(s)*(-s*alpha1*(s+thetac)^2*Dp^(3/2)-thetac*(Dc-2*Dp)*s^(5/2)+(-Dc+Dp)*s^(7/2)+s^(3/2)*Dp*thetac^2+sqrt(Dp)*s^2*Dc*alpha1*(s+thetac))*exp(-sqrt(s)*x/sqrt(Dp))+alpha1*(s+thetac)*(-pinf*s-pinf*thetac+A2)*Dp^(3/2)+(-pinf*(Dc-2*Dp)*thetac+A2*(Dc-Dp))*s^(3/2)-pinf*(Dc-Dp)*s^(5/2)-s*alpha1*Dc*(-pinf*s-pinf*thetac+A2)*sqrt(Dp)-sqrt(s)*Dp*thetac*(-pinf*thetac+A2))*sqrt(s+thetac))/((s+thetac)^(3/2)*s*((Dc-Dp)*s-Dp*thetac)*(sqrt(Dp)*alpha1-sqrt(s)))

q(x, s) = -(-(-thetac*s^(3/2)-s^(5/2)+(s^2+s*thetac)*alpha1*Dp^(1/2))*Dc*A1*exp((lh-x)*(s+thetac)^(1/2)/Dc^(1/2))+((alpha1*(s+thetac)*(-pinf*s-pinf*thetac+A2)*Dp^(3/2)+s*Dp^(1/2)*(A1*(s+thetac)*Dc^(1/2)-Dc*alpha1*(-pinf*s-pinf*thetac+A2)))*(s+thetac)^(1/2)+A1*Dp^(1/2)*s*Dc*alpha1*(s+thetac))*exp(s^(1/2)*(-lh+x)/Dp^(1/2))-(-_F1(s)*(-s*alpha1*(s+thetac)^2*Dp^(3/2)-s^(3/2)*Dp*thetac^2+thetac*(Dc-2*Dp)*s^(5/2)+(Dc-Dp)*s^(7/2)+Dp^(1/2)*s^2*Dc*alpha1*(s+thetac))*exp((-2*lh+x)*s^(1/2)/Dp^(1/2))+_F1(s)*(-s*alpha1*(s+thetac)^2*Dp^(3/2)-thetac*(Dc-2*Dp)*s^(5/2)+(-Dc+Dp)*s^(7/2)+s^(3/2)*Dp*thetac^2+Dp^(1/2)*s^2*Dc*alpha1*(s+thetac))*exp(-s^(1/2)*x/Dp^(1/2))+alpha1*(s+thetac)*(-pinf*s-pinf*thetac+A2)*Dp^(3/2)+(-pinf*(Dc-2*Dp)*thetac+A2*(Dc-Dp))*s^(3/2)-pinf*(Dc-Dp)*s^(5/2)-s*alpha1*Dc*(-pinf*s-pinf*thetac+A2)*Dp^(1/2)-s^(1/2)*Dp*thetac*(-pinf*thetac+A2))*(s+thetac)^(1/2))/((s+thetac)^(3/2)*s*((Dc-Dp)*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2)))

(1)

"(=)"

q(x, s) = s*_F1(s)*Dp^(1/2)*Dc*alpha1*thetac/((s+thetac)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2))*exp(s^(1/2)*x/Dp^(1/2)))+exp(s^(1/2)*x/Dp^(1/2))*A2*Dc*alpha1*Dp^(1/2)/((s+thetac)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2))*exp(s^(1/2)*lh/Dp^(1/2)))-exp(s^(1/2)*x/Dp^(1/2))*A1*thetac*Dc^(1/2)*Dp^(1/2)/((s+thetac)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2))*exp(s^(1/2)*lh/Dp^(1/2)))-s^2*_F1(s)*exp(s^(1/2)*x/Dp^(1/2))*Dp^(1/2)*Dc*alpha1/((s+thetac)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2))*(exp(s^(1/2)*lh/Dp^(1/2)))^2)-s*exp(s^(1/2)*x/Dp^(1/2))*Dc*alpha1*pinf*Dp^(1/2)/((s+thetac)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2))*exp(s^(1/2)*lh/Dp^(1/2)))+2*exp(s^(1/2)*x/Dp^(1/2))*Dp^(3/2)*alpha1*pinf*thetac/((s+thetac)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2))*exp(s^(1/2)*lh/Dp^(1/2)))+s*Dc*A1*exp((s+thetac)^(1/2)*lh/Dc^(1/2))*Dp^(1/2)*alpha1/((s+thetac)^(3/2)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2))*exp((s+thetac)^(1/2)*x/Dc^(1/2)))+exp(s^(1/2)*x/Dp^(1/2))*Dp^(3/2)*alpha1*pinf*thetac^2/((s+thetac)*s*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2))*exp(s^(1/2)*lh/Dp^(1/2)))-exp(s^(1/2)*x/Dp^(1/2))*A2*Dp^(3/2)*alpha1*thetac/((s+thetac)*s*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2))*exp(s^(1/2)*lh/Dp^(1/2)))-s*exp(s^(1/2)*x/Dp^(1/2))*A1*Dc*alpha1*Dp^(1/2)/((s+thetac)^(3/2)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2))*exp(s^(1/2)*lh/Dp^(1/2)))+_F1(s)*exp(s^(1/2)*x/Dp^(1/2))*alpha1*Dp^(3/2)*thetac^2/((s+thetac)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2))*(exp(s^(1/2)*lh/Dp^(1/2)))^2)+2*s*_F1(s)*exp(s^(1/2)*x/Dp^(1/2))*alpha1*Dp^(3/2)*thetac/((s+thetac)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2))*(exp(s^(1/2)*lh/Dp^(1/2)))^2)-exp(s^(1/2)*x/Dp^(1/2))*A1*Dc*alpha1*thetac*Dp^(1/2)/((s+thetac)^(3/2)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2))*exp(s^(1/2)*lh/Dp^(1/2)))+Dc*A1*exp((s+thetac)^(1/2)*lh/Dc^(1/2))*Dp^(1/2)*alpha1*thetac/((s+thetac)^(3/2)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2))*exp((s+thetac)^(1/2)*x/Dc^(1/2)))-exp(s^(1/2)*x/Dp^(1/2))*Dc*alpha1*pinf*thetac*Dp^(1/2)/((s+thetac)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2))*exp(s^(1/2)*lh/Dp^(1/2)))-s*_F1(s)*exp(s^(1/2)*x/Dp^(1/2))*Dp^(1/2)*Dc*alpha1*thetac/((s+thetac)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2))*(exp(s^(1/2)*lh/Dp^(1/2)))^2)-s^(3/2)*Dc*pinf/((s+thetac)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2)))-s^(1/2)*A2*Dp/((s+thetac)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2)))+s^(3/2)*Dp*pinf/((s+thetac)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2)))+s^(1/2)*A2*Dc/((s+thetac)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2)))+s*Dc*alpha1*pinf*Dp^(1/2)/((s+thetac)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2)))+A2*Dp^(3/2)*alpha1*thetac/((s+thetac)*s*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2)))-2*Dp^(3/2)*alpha1*pinf*thetac/((s+thetac)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2)))-A2*Dc*alpha1*Dp^(1/2)/((s+thetac)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2)))-s^(3/2)*Dc*A1*exp((s+thetac)^(1/2)*lh/Dc^(1/2))/((s+thetac)^(3/2)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2))*exp((s+thetac)^(1/2)*x/Dc^(1/2)))-s^2*_F1(s)*alpha1*Dp^(3/2)/((s+thetac)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2))*exp(s^(1/2)*x/Dp^(1/2)))-s^(3/2)*_F1(s)*thetac*Dc/((s+thetac)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2))*exp(s^(1/2)*x/Dp^(1/2)))+s^(5/2)*_F1(s)*exp(s^(1/2)*x/Dp^(1/2))*Dp/((s+thetac)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2))*(exp(s^(1/2)*lh/Dp^(1/2)))^2)-s^(5/2)*_F1(s)*exp(s^(1/2)*x/Dp^(1/2))*Dc/((s+thetac)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2))*(exp(s^(1/2)*lh/Dp^(1/2)))^2)+2*s^(3/2)*_F1(s)*thetac*Dp/((s+thetac)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2))*exp(s^(1/2)*x/Dp^(1/2)))+s^(1/2)*_F1(s)*Dp*thetac^2/((s+thetac)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2))*exp(s^(1/2)*x/Dp^(1/2)))-Dp^(3/2)*alpha1*pinf*thetac^2/((s+thetac)*s*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2)))+A2*Dp^(3/2)*alpha1/((s+thetac)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2)))-s*Dp^(3/2)*alpha1*pinf/((s+thetac)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2)))-s^(1/2)*Dc*pinf*thetac/((s+thetac)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2)))+2*s^(1/2)*Dp*pinf*thetac/((s+thetac)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2)))+Dp*pinf*thetac^2/((s+thetac)*s^(1/2)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2)))-A2*Dp*thetac/((s+thetac)*s^(1/2)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2)))-s^(5/2)*_F1(s)*Dc/((s+thetac)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2))*exp(s^(1/2)*x/Dp^(1/2)))+s^(5/2)*_F1(s)*Dp/((s+thetac)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2))*exp(s^(1/2)*x/Dp^(1/2)))+Dc*alpha1*pinf*thetac*Dp^(1/2)/((s+thetac)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2)))-s^(1/2)*Dc*A1*exp((s+thetac)^(1/2)*lh/Dc^(1/2))*thetac/((s+thetac)^(3/2)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2))*exp((s+thetac)^(1/2)*x/Dc^(1/2)))+s*exp(s^(1/2)*x/Dp^(1/2))*Dp^(3/2)*alpha1*pinf/((s+thetac)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2))*exp(s^(1/2)*lh/Dp^(1/2)))-exp(s^(1/2)*x/Dp^(1/2))*A2*Dp^(3/2)*alpha1/((s+thetac)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2))*exp(s^(1/2)*lh/Dp^(1/2)))-s*exp(s^(1/2)*x/Dp^(1/2))*A1*Dc^(1/2)*Dp^(1/2)/((s+thetac)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2))*exp(s^(1/2)*lh/Dp^(1/2)))+s^2*_F1(s)*exp(s^(1/2)*x/Dp^(1/2))*alpha1*Dp^(3/2)/((s+thetac)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2))*(exp(s^(1/2)*lh/Dp^(1/2)))^2)+s^(1/2)*_F1(s)*exp(s^(1/2)*x/Dp^(1/2))*Dp*thetac^2/((s+thetac)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2))*(exp(s^(1/2)*lh/Dp^(1/2)))^2)-s^(3/2)*_F1(s)*exp(s^(1/2)*x/Dp^(1/2))*thetac*Dc/((s+thetac)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2))*(exp(s^(1/2)*lh/Dp^(1/2)))^2)+2*s^(3/2)*_F1(s)*exp(s^(1/2)*x/Dp^(1/2))*thetac*Dp/((s+thetac)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2))*(exp(s^(1/2)*lh/Dp^(1/2)))^2)-2*s*_F1(s)*alpha1*Dp^(3/2)*thetac/((s+thetac)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2))*exp(s^(1/2)*x/Dp^(1/2)))-_F1(s)*alpha1*Dp^(3/2)*thetac^2/((s+thetac)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2))*exp(s^(1/2)*x/Dp^(1/2)))+s^2*_F1(s)*Dp^(1/2)*Dc*alpha1/((s+thetac)*(Dc*s-Dp*s-Dp*thetac)*(Dp^(1/2)*alpha1-s^(1/2))*exp(s^(1/2)*x/Dp^(1/2)))

(2)

"(=)"

q(x, s) = (A1*(-thetac*s^(3/2)*Dp^(1/2)*alpha1-s^(5/2)*Dp^(1/2)*alpha1+s^2*(s+thetac))*Dc*exp((lh-x)*(s+thetac)^(1/2)/Dc^(1/2))+((-alpha1*((2*pinf*thetac-A2)*s^(3/2)+s^(5/2)*pinf+thetac*s^(1/2)*(pinf*thetac-A2))*Dp^(3/2)+Dp^(1/2)*((A1*thetac*Dc^(1/2)+Dc*alpha1*(pinf*thetac-A2))*s^(3/2)+s^(5/2)*(Dc*alpha1*pinf+Dc^(1/2)*A1)))*(s+thetac)^(1/2)+Dp^(1/2)*A1*Dc*alpha1*(thetac*s^(3/2)+s^(5/2)))*exp(s^(1/2)*(-lh+x)/Dp^(1/2))+(s+thetac)^(1/2)*((-alpha1*(thetac^2*s^(3/2)+2*thetac*s^(5/2)+s^(7/2))*Dp^(3/2)+thetac*s^(5/2)*Dp^(1/2)*Dc*alpha1+s^(7/2)*Dp^(1/2)*Dc*alpha1+((Dc-Dp)*s-Dp*thetac)*s^2*(s+thetac))*_F1(s)*exp((-2*lh+x)*s^(1/2)/Dp^(1/2))+(alpha1*(thetac^2*s^(3/2)+2*thetac*s^(5/2)+s^(7/2))*Dp^(3/2)-thetac*s^(5/2)*Dp^(1/2)*Dc*alpha1-s^(7/2)*Dp^(1/2)*Dc*alpha1+((Dc-Dp)*s-Dp*thetac)*s^2*(s+thetac))*_F1(s)*exp(-s^(1/2)*x/Dp^(1/2))+alpha1*((2*pinf*thetac-A2)*s^(3/2)+s^(5/2)*pinf+thetac*s^(1/2)*(pinf*thetac-A2))*Dp^(3/2)-Dp^(1/2)*Dc*alpha1*(pinf*thetac-A2)*s^(3/2)-s^(5/2)*Dc*alpha1*pinf*Dp^(1/2)+(pinf*s+pinf*thetac-A2)*((Dc-Dp)*s-Dp*thetac)*s))/(s^(3/2)*(s+thetac)^(3/2)*(-Dp^(1/2)*alpha1+s^(1/2))*((Dc-Dp)*s-Dp*thetac))

(3)

``


 

Download coefficients.mw

you may want

It seems very simple idea from Maple point of view. You wanted an answer for an impossible question.. Integration of the given function is not possible. Integration of Product of inverse of x and inverse of sin(x). not obtainable by any method so far.

When you say substitute in the solution, it substitutes first for x in the denominator (right decision not to substitute for sin(x) because you did not say so!). Now it is simple integration wrt to t. Integration of (1/t) sin-1x dx. After the solution is obtained you should now know that t was substituted for getting the answer. Hence it resubstitutes x for t which was constant so far and t equal to x as per our advise! Note Maple knows both t and x cannot be substituted at once for this very strange problem!!

 

NULL

Maple could not get an answer as an expression here. Hence retains it.

1/(x*sin(x))

(1)

"(->)"

int(1/(x*sin(x)), x)

(2)

"="

int(1/(x*sin(x)), x)

(3)

NULLNULL

 

NULL

You have said substitute t for x. It substitutes  for x only strictly as per our order!

int(1/(t*sin(x)), x)

ln(csc(x)-cot(x))/t

(4)

NULL

Now again we have given the freedom to substitute for x = t. It quitely returns the t back to x to suit its convenience!.

The answer is hence

int(1/(t*sin(x)), x)

nt(1/(t*sin(x)), x)

(5)

NULL

OR

int(1/(x*sin(t)), t)

ln(csc(t)-cot(t))/x

(6)

OR

int(1/(x*sin(t)), x)

ln(x)/sin(t)

(7)

NULL

OR

int(1/(t*sin(x)), t)

ln(t)/sin(x)

(8)

NULL


 

Download MyAnswer.mw

Download Answer.mwAnswer.mw

  

ContourPlotAnswer.mw
Hope this answers your doubt. Thanks. Ramakrishnan V

contourplot(4*lambda2*result^2/(Pi*(lambda2+1)^2)-lambda1, lambda1 = 0 .. 1, lambda2 = 0 .. 1, contours = [0], axes = boxed, title = tit, titlefont = [SYMBOL, 16], thickness = 1, color = black, font = [1, 1, 18], tickmarks = [2, 4], linestyle = 1, view = [0.2e-2 .. 1, 0.2e-2 .. 1])
NULL

NULL

I have obtained the function in terms of λ1 and λ2 and used in countour plot. It gives approx function for Result in the plot by mouse hovering over it.

NULL

Result := (`λ__1`*Pi*(`λ__2`+1)^2/(4*`λ__2`))^.5

with(plots)

contourplot(Result, `λ__1` = 0 .. 1, `λ__2` = 0 .. 1)

 

NULL

NULL


 

Download ContourPlotAnswer.mw

 

 

 

@Kitonum 

Ramakrishnan V

rukmini_ramki@hotmail.com

enclosed doc substitutes but the additional data comes with it.

What could they be. How to suppress them?

Thanks

Ramakrishnan V
 

my_proc := proc (func::`+`) ` `*` ` .. ` `*` `*subs([x[1] = 2, x[2] = 1], func) end proc; func := x[1]*x[2]+10*x[1]+5; my_proc(func)

` `^2 .. 27*` `^2

(1)

my_proc(x[1]+x[2])

` `^2 .. 3*` `^2

(2)

x[3] := 5; my_proc(x[3]+x[2])

` `^2 .. 6*` `^2

(3)

my_proc := proc (func::`+`) ` `*` `*` `*subs([x[1] = 2, x[2] = 1], func) end proc; func := x[1]*x[2]+10*x[1]+5; my_proc(func)

27*` `^3

(4)

``

``


 

Download substitutes.mw    substitutes.mw

Since a link was not provided, I assume the problem is to bring the cursor to any position on the screen. As you rightly said, use the vertical scroll on the right side to anywhere you want, not only on the cyurrent page, but on the entire file itself, and left click at the required point. This is the easiest way to process. Enter key is not for this purpose as this would evaluate the codes (or no codes) and go to the next space. It may at times add a line which was not intended.

Vertical with mouse pointer and left click is the simplest solution in my opinion.

Hope the answer is liked.

Cheers.

Ramakrishnan V

Dear Sir,

My answer would be

The constant 3 from the integral 3 x2 dx is taken out and then integrated by maple. Then mutipling the answer by 3 would add the constant term also mutiplied by 3.

Hope this is correct.

Thanks.

Ramakrishnan V

Your codes are correct except that in dsolve command, there are three terms. hence should be in square brackets as these form a list of equations.

i attach the doc as corrected.
 

F := proc (t) options operator, arrow; piecewise(t < 0, 0, t < 1, 100, t < 2, 200, t < 3, 50) end proc

proc (t) options operator, arrow; piecewise(t < 0, 0, t < 1, 100, t < 2, 200, t < 3, 50) end proc

(1)

plot(proc (t) options operator, arrow; piecewise(t < 0, 0, t < 1, 100, t < 2, 200, t < 3, 50) end proc)

 

sol1 := dsolve([diff(y(t), t, t)+4*(diff(y(t), t))-3*y(t) = F, (D(y))(0) = 1, y(0) = 0])

y(t) = (1/42)*exp((-2+7^(1/2))*t)*(2*7^(1/2)+7)*(F+7^(1/2)-2)-(1/42)*exp(-(2+7^(1/2))*t)*(-7+2*7^(1/2))*(F-2-7^(1/2))-(1/3)*F

(2)

 

 

 

``


 

Download corrected1.mwcorrected1.mw

the two equations are a perfect solution set.

All you need is values of any  3 variables and the remaining variable values will be determined by maple.

The remaining equations are only derived ones and hence redundant and will not help you find the answer in any better way.

I attach a doc to help you understand my statements.

Hope I am correct(!).

Cheers.

Ramakrishnan Vset_of_equations.mw
 

restart

v := a*t+u

a*t+u

(1)

s := u*t+.5*a*t^2``

u*t+.5*a*t^2

(2)

t := 3

3

(3)

solve( {v=10,s=20}, {u,a});

{a = 2.222222222, u = 3.333333333}

(4)

a

a

(5)

restart

v := a*t+u

a*t+u

(6)

s := u*t+.5*a*t^2NULL

u*t+.5*a*t^2

(7)

a := 2.222

2.222

(8)

solve( {v=10,s=20}, {u,t});

{t = 2.999700090, u = 3.334666400}, {t = 6.001200000, u = -3.334666400}

(9)

restart

v := a*t+u

a*t+u

(10)

s := u*t+.5*a*t^2``

u*t+.5*a*t^2

(11)

u := 3.33

3.33

(12)

solve( {v=10,s=20}, {a,t});

{a = 2.222777500, t = 3.000750188}

(13)

``


 

Download set_of_equations.mw

.

Please find attached my doc explaining you three ways of plotting what you desired under the conditions x^2+y^2=1

assuming is a maple command with which you can do wonders!

Ramakrishnan V

RangeInputExample.mw
 

``

``

``

NULL

z := `assuming`([x^3-2*x^2*y], [x^2+y^2 = 1])

x^3-2*x^2*y

(1)

"->"

 

``

 

``

plot3d(`assuming`([x^3-2*x^2*y], [x^2+y^2 = 1]), x = -4 .. 4, y = -4 .. 4, axes = normal, numpoints = 5000)

 

plot3d(x^3-2*x^2*y, x = -sqrt(-y^2+1) .. sqrt(-y^2+1), y = -1 .. 1, axes = normal, numpoints = 5000)

 

``


 

Download RangeInputExample.mw

 

Just right click the graph anywhere,

A menu box will pop up.

Select axes (left click) Another nine line menu pops up.

Select labels (left click)Another four  line menu pops up.

Select edit vertical (left click)

Now the tricky answer to your question.

Enter as many spaces as you want after the Ubar. You will get this Ubar distanced from y axis. In the same way enter the enter key as many times as you want the distance below x axis.LabelPosition_in_plottingVRK.mw
 

y = x^2-1

smartplot(rhs(y = x^2-1))

 

``

``


 

Download LabelPosition_in_plottingVRK.mw

 

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